Which of the following is a disadvantage to using equations?
An equation, a table of values, a set of ordered pairs, and a graph of the equation are all different representations of the same mathematical relationship. The equation defines the relationship between variables, while the table of values lists specific input-output pairs derived from the equation. These pairs can be expressed as ordered pairs (x, y), which can then be plotted on a graph to visually represent the relationship. Together, they provide a comprehensive understanding of the equation's behavior.
The graph of an equation is a visual representation of the values that satisfy the equation.
To determine if a relationship is linear from a table, check if the differences in the y-values (output) corresponding to equal differences in the x-values (input) are constant. For a graph, a linear relationship will appear as a straight line. In an equation, if the equation can be expressed in the form (y = mx + b), where (m) and (b) are constants, it indicates a linear relationship.
You could put the equation in slope-intercept form or in parent linear function or even make a table of values.
Just like any other equation, you can set up a table of x values, and calculate the corresponding y values. Then plot the points on the graph. In this case, it helps to have some familiarity with quadratic equations (you can find a discussion in algebra books), and recognize (from the form of the equation) whether your quadratic equation represents a parabola, a circle, an ellipse, or a hyperbola.
An equation, a table of values, a set of ordered pairs, and a graph of the equation are all different representations of the same mathematical relationship. The equation defines the relationship between variables, while the table of values lists specific input-output pairs derived from the equation. These pairs can be expressed as ordered pairs (x, y), which can then be plotted on a graph to visually represent the relationship. Together, they provide a comprehensive understanding of the equation's behavior.
The graph of an equation is a visual representation of the values that satisfy the equation.
To determine if a relationship is linear from a table, check if the differences in the y-values (output) corresponding to equal differences in the x-values (input) are constant. For a graph, a linear relationship will appear as a straight line. In an equation, if the equation can be expressed in the form (y = mx + b), where (m) and (b) are constants, it indicates a linear relationship.
Depends what the graph is.
You could put the equation in slope-intercept form or in parent linear function or even make a table of values.
A table you make to find the coordinates to graph.
There are three ways: a table, a graph, and an equation.
Just like any other equation, you can set up a table of x values, and calculate the corresponding y values. Then plot the points on the graph. In this case, it helps to have some familiarity with quadratic equations (you can find a discussion in algebra books), and recognize (from the form of the equation) whether your quadratic equation represents a parabola, a circle, an ellipse, or a hyperbola.
Any explanation will depend on whether or not the table of values and the graph are related to one another. Nothing in the question indicates that they are.
I would set up a table of values and calculate several of the values of the variables (I would try to calculate the "interesting" values setting one to zero and calculating the other(s), guessing at a maximum or minimum value etc. Then I would plot the values on graph paper.
Graph and Table: http://i50.tinypic.com/szhr4k.png
The equation which remains true for each set of variables in the table.